Space of modular forms of level 320, weight 2, and Character 320.c

• Label: 320.2.c
• Level: $320$
• Weight: $2$
• Character orbit: 320.c
• Rep. character: $\chi_{320}(129,\cdot)$
• Character field: $\Q$
• Dimension: $10$
• Newform subspaces: $4$
• Sturm bound: $96$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 320 = 2^{6} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	320.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(96\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(3\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(320, [\chi])\).

	Total	New	Old
Modular forms	60	14	46
Cusp forms	36	10	26
Eisenstein series	24	4	20

Trace form

\( 10 q + 2 q^{5} - 10 q^{9} - 8 q^{21} + 2 q^{25} + 4 q^{29} - 12 q^{41} + 30 q^{45} - 2 q^{49} + 20 q^{61} + 16 q^{65} - 72 q^{69} + 18 q^{81} - 32 q^{85} - 28 q^{89}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(320, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
320.2.c.a	$320$	$2$	320.c	5.b	$2$	$2$	$2$	$2.555$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)					160.2.c.a	$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q+(\beta-1)q^{5}+3 q^{9}+2\beta q^{13}+4\beta q^{17}+\cdots\)
320.2.c.b	$320$	$2$	320.c	5.b	$2$	$2$	$2$	$2.555$	\(\Q(\sqrt{-1}) \)	None					40.2.c.a	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{3}+(\beta+1)q^{5}+\beta q^{7}-q^{9}+\cdots\)
320.2.c.c	$320$	$2$	320.c	5.b	$2$	$2$	$2$	$2.555$	\(\Q(\sqrt{-1}) \)	None					40.2.c.a	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{3}+(-\beta+1)q^{5}+\beta q^{7}-q^{9}+\cdots\)
320.2.c.d	$320$	$2$	320.c	5.b	$2$	$4$	$4$	$2.555$	\(\Q(i, \sqrt{5})\)	\(\Q(\sqrt{-5}) \)			✓		160.2.c.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{1}q^{3}+\beta _{2}q^{5}-\beta _{3}q^{7}+(-3+2\beta _{2}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(320, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(320, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 2}\)